Resonance and chaos in the stochastic Mackey-Glass equation

Abstract: The study focuses on noise-induced phenomena in stochastic Mackey-Glass equations. In the weak nonlinearity region, the standard stochastic resonances (SRs) switching between two point, periodic, and chaotic attractors are observed with the negative largest Lyapunov exponent. The numerically computed resonant period deviates from the classical estimation based on time delays and we provide a more precise estimation based on a linear mode analysis of the existing unstable spiral. In the strong nonlinearity region, we newly discover high-dimensional chaotic SR with multiple positive Lyapunov exponents, which has not been previously reported. Unlike the dynamics in the weak nonlinearity region, the point of resonance precedes the zero-crossing point of the largest Lyapunov exponent, resulting in the coexistence of high-dimensional stochastic chaos and SR.